兩種Regularized NS方程之大渦紊流模型評估

Abstract

本論文主要是探討紊流模型之特性,並將分析之結果與原始不可壓縮黏性Navier-Stokes方程組做一比較。在求解統御方程式方面,論文是架構在二維正交座標系統上，並於非交錯式網格(non-staggered grids)上壓力與速度耦合配置方式下,採用有限差分方法(finite-difference method)來離散統御方程式,以期精確的求解流體力學方程式。 紊流模型的基礎,是建立在變更非線性不可壓縮Navier-Stokes方程中的對流項(convective term)或擴散項(diffusion term),藉由調整此兩項在動量方程式中所佔的比例,除了抑制其非線性的成長外,也希望能使用較少成本(較粗網格或較少計算時間),捕捉我們必須使用較高成本來計算非線性不可壓縮Navier-Stokes方程才能觀察到的流場狀況,這樣的作法我們稱之為規則化(regularization)。 本研究討論了Leray-alpha及Navier-Stokes-alpha兩種紊流模型,此兩種紊流模型除了方程形式類似外,也相同的改變動量方程式中的對流項。透過數值模擬,我們期望了解使用紊流模型的益處,以及與原始非線性不可壓縮Navier-Stokes方程之差異。

This thesis explores and analyzes the characteristics of Turbulence Models by comparing the results with original incompressible viscous Navier-Stokes equations.This thesis is constructed from the two-dimensional in orthogonal non-staggered grids in pressure and velocity coupling configuration mode, to discretize the governing equations by finite-difference method, to make computational fluid dynamic equations for precisely. Turbulence model is based on the changes of nonlinear incompressible Navier-Stokes equations in convective terms or diffusion terms and adjust their ratio in the momentum equations.In addition, we want to suppress its non-linear growth, but also hope to use a less cost (coarse grid or less computing time) to obtain information about turbulent flow, rather than using a high cost to solve the nonlinear incompressible Navier-Stokes equations. This approach is called Regularization. This study discusses two turbulence models: Leray-alpha model and Navier-Stokes-alpha model. These two turbulence models are similar. They both change the momentum equations convection terms.Through numerical simulation, we expect to understand the benefits of there turbulence models. We also hope to know the differences between them and the original non-linear incompressible Navier-Stokes equations.